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For mathematics you have to have mathematics or computer science at your graduation level.
May be in some institutes they may qualify Electrical and Electronics Engineering for this course.
You please check some institutes qualification criteria for mathematics before making any decision.

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You are eligible there. So please first check education qualification of the course and institute in which you want to take admission. Education qualification criteria is different for different institutes.

Most probably no.
Electronics discipline is not allowed in Mathematics discipline but Mathematics discipline is allowed in Electronics discipline.
However eligibility criteria depends upon the educational institute in which you want to take admission so please first check the education qualification of that institute in which you want to take admission and the respective course in which you want to take admission.

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You are eligible there. So please first check education qualification of the course and institute in which you want to take admission. Education qualification criteria is different for different institutes.

First you need to complete your masters in order to attend GATE exam.
GATE exam actually now a days have two applications :
(1) get admission into Higher education programs (like M Tech/ PHd)
(2) Job in some PSUs/Govt organiations

There are very few PSUs which will recruit a candidate which have qualified GATE with mathematics subject.
So main advantage in case you of would be that you can get admission in IISc/IITs or any reputed college using this GATE score for higher education.

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For important subjects and topics buy a previous years papers book in which you will find all the analysis very well including GATE 2015 paper.
GATE 2016 Reference Books : http://www.gate2016.info/gate-2016-books/

First you have to have a book of previous GATE 20-30 years papers with solution so that you can get a good idea about GATE questions.
Then atleast one standard book of each subject. All books required for GATE exam preparation in Engineering are mentioned in above link.
we can give you some suggestion for your preparation time table :
(1) make plan as per time availability in a day for study exclude other times like daily routine work etc.
(2) Always study in three level anything :
1. easy
2. medium
3. Hard

First follow easy. Like you are going to study a chapter. Note down all the important topic from exam point of view and study introductory of every topic then move to next chapter and so on. It will not take much time and you will complete your whole syllabus at least once then medium than hard.

Make a time table for a whole day, for a week, for a month and for a year for GATE 2016. Stick to the time table. Must include time for revision in each time table.

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There are mainly two applications of GATE exam for a candidate :
(1) Job in PSU or govt sector using GATE score
(2) Higher Education using GATE score

(1) As far as I know there are very less PSUs which recruit Mathematician on the basis of GATE score But there are few Govt departments for which you can apply on the basis of your M. Sc. also there your GATE score card will have no use but if there is any interview they will surely consider your GATE/NET score card if you have good one.
You can find such high profile and reputed govt. jobs in UPSC & SSC special recruitment notification also. UPSC ask about your GATE/NET score while filling application form.

For any PSU application through GATE there are two kind of restriction for a candidate.
First in which branch candidate have done B Tech degree.
Second in which GATE paper he/she appeared.

Point to be noted here is they need a candidate with both of these combine correctly.
When you will go through any notification of any PSU which recruit through GATE then you will find that they mention GATE paper for particular post as well as your B Tech degree for that particular post.

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Sir,
I am pursuing M.Sc final in maths. Can I eligible for GATE exam and if yes then which course I need to apply for GATE that would help me in future? And what is the use of GATE for me?
Also after my schooling there is a year lag in my career.

Last date of application form filling was 8 Oct. So you would not be able to fill your form now.
Yes final year candidates of M Sc were eligible for GATE 2016. As you mentioned your are pursuing M.Sc in maths so it would be better if you choose M tech or M tech + P HD in maths after qualifying GATE.

There are two main uses of qualifying GATE exam :
1. Getting job in PSUs
2. Getting admission for Higher education

Gap will not affect your career much. If you don’t let it affect your career much.

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Hello sir,
I completed three years in b-tech graduation in electronics and communication and I did engineering mathematics in one of my semesters. can I apply for MA paper in GATE and try for IIT’s ? If yes, In which stream will I have to pursue M-TECH? Please check and inform me about the qualification criteria to get into IIT’s or any such institutes.